EXERCISE DESIGN OF EXPERIMENTS
Dikerjakan berkelompok, tiap kelompok terdiri dari 3 orang. Jika tidak genap,
diperbolehkan beberapa kelompok beranggotakan 4 orang.
Perhitungan dilakukan secara manual (tanpa bantuan software statistika, e.g.
Minitab) dan jawaban boleh menggunakan bahasa Indonesia maupun bahasa
Inggris.
Jawaban lengkap ditulis di kertas dobel folio dan dikumpulkan ke ketua kelas
paling lambat hari Jumat, 20 Maret 2015 pukul 18.00 WIB.
1. In Design and Analysis of Experiments, 5th edition (John Wiley & Sons,
2001), D. C. Montgomerry describes an experiment in which the tensile
strength of a synthetic fiber is of interest to the manufacturer. It is
suspected that strength is related to the percentage of cotton in the fiber.
Five levels of cotton percentage are used, and five replicates are run in
random order, resulting in the data below.
Cotton
Percentage
Observations
1 2 3 4
5
15 7 7 15 11 9
20 12 17 12 18 18
25 14 18 18 19 19
30 19 25 22 19 23
35 7 10 11 15 11
a) Does cotton percentage affect breaking strength? Draw comparative
box plots and perform an analysis of variance. Use = 0.05.
b) Plot average tensile strength against cotton percentage and interpret
the results.
c) Analyze the residuals and comment on model adequacy.
2. An electronics engineer is interested in the effect on tube conductivity of
five different types of coating for cathode ray tubes in a
telecommunications system display device. The following conductivity
data are obtained.
Coating
Type Conductivity
1 143 141 150 146
2 152 149 137 143
3 134 133 132 127
4 129 127 132 129
5 147 148 144 142
a) Is there any difference in conductivity due to coating type? Use =
0.01.
b) Analyze the residuals from this experiment.
c) Construct a 95% interval estimate of the coating type 1 mean.
Construct a 99% interval estimate of the mean difference between
coating types 1 and 4.
3. An article in the ACI Materials Journal (Vol. 84, 1987, pp. 213-216)
describes several experiments investigating the rodding of concrete to
remove entrapped air. A 3-inch X 6-inch cylinder was used, and the
number of times this rod was used is the design variable. The resulting
compressive strength of the concrete specimen is the response. The data
are shown in the following table.
Rodding
Level Compressive Strength
10 1530 1530 1440
15 1610 1650 1500
20 1560 1730 1530
25 1500 1490 1510
a) Is there any difference in compressive strength due to the rodding
level?
b) Find the P-value for the F-statistic in part a)
c) Analyze the residuals from this experiment. What conclusions can you
draw about the underlying model assumptions?
4. The compressive strength of concrete is being studied, and four different
mixing techniques are being investigated. The following data have been
collected.
Mixing
Technique Compressive Strength (psi)
1 3129 3000 2865 2890
2 3200 3300 2975 3150
3 2800 2900 2985 3050
4 2600 2700 2600 2765
a) Test the hypothesis that mixing techniques affect the strength of the
concrete. Use = 0.05.
b) Find the P-value for the F-statistic computed in part a).
c) Analyze the residuals from this experiment.
5. A paper in the Journal of the Association of Asphalt Paving Technologists
(Vol. 59, 1990) describes an experiment to determine the effect of air
voids on percentage retained strength of asphalt. For purposes of the
experiment, air voids are controlled at three levels; low (2-4%), medium
(4-6%), and high (6-8%). The data are shown in the following table.
Air Voids Retained Strength (%)
Low 106 90 103 90 79 88 92 95
Medium 80 69 94 91 70 83 87 83
High 78 80 62 69 76 85 69 85
a) Do the different levels of air voids significantly affect mean retained
strength? Use = 0.01.
b) Find the P-value for the F-statistic in part a).
c) Analyze the residuals from this experiment.
d) Find a 95% confidence interval on mean retained strength where
there is a high level of air voids.
e) Find a 95% confidence interval on the difference in mean retained
strength at the low and high levels of air voids.
-Good Luck-